1. Member of the Editorial Board of the Journal of “Acta of Math Sinica” (Editorial Department in Beijing)

2. Member of the Editorial Board of the Journal of “J. of Pure and Applied Math.”(Editorial Department in Xian)

3. Member of the Editorial Board of the Journal of “Northeastern Mathematical Journal” (Editorial Department in Jilin University, Changchun)

4. Member of the Editorial Board of the Journal of Partial Differential Equations, (Editorial Department in Peking University, Beijing)

5. Member of the Editorial Board of the Journal of Kinetic and Related Models, AIMS.

6. Member of the Editorial Board of the International J. of Numerical Analysis and Modeling, ISCI.

7．Member of the Editorial Board of the J. of Pseudo-Differential Operators and Applications, Birkhauser.

8. Member of the Editorial Board of the J. of Wuhan University (Natural Science English Edition)

9. Member of the Editorial Board of the Acta Mathematica Scientia

10. Member of the Editorial Board of the J. Applied Mathematics

11. Editor in chief of the “J. of Mathematics” (Editorial Department in Wuhan University)

12. Member of National Key Scientific Project Group “The General Theory of Partial Differential Equations” (Sponsored by the National Natural Science Foundation of China, from Jan. of 1991 - Dec. of 1995)

13. Member of National Key Scientific Project Group “The Modern Analysis Theory of Partial Differential Equations” (Sponsored by the National Natural Science Foundation of China, from Jan. of 1996 - Dec. of 2000)

14. Member of National Key Research 973 Grants (Sponsored by the National Ministry of Science and Technology of China, from Nov. of 1999 - Dec. of 2006).

15. National Excellent Young Scientist' Grants, (Sponsored by the National Natural Science Foundation of China, from Jan. 2001-Dec. 2004).

16. Member of National Key Scientific Project Group “Nonlinear Elliptic and Parabolic Partial Differential Equations” (Sponsored by the National Natural Science Foundation of China, from Jan. of 2007 - Dec. of 2010)

17. Head of National Key Scientific Project Group “Nonlinear Elliptic and Parabolic Partial Differential Equations” (Sponsored by the National Natural Science Foundation of China, from Jan. of 2012 - Dec. of 2016)

**Main Research Interests:**

1. The theory of spectral asymptotics for elliptic operator and Schrodinger operator, scattering theory (in particular the drums are fractal)

2. Linear and non-linear microlocal analysis

3. Applications of PDE (e.g. reaction-diffusion equations etc.)

4. Theory of singular PDEs and theory of degenerate PDEs.

**Main Paper List (2001-2014)**

1. A characterization for Gevrey-Sobolev wave front set, Acta Math. Sinica, English Series, 17(2), 295-300 (2001).

2. (with Luo Zhuangchu and H. Tahara, Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity, Ann. Fourier Inst., Vol.51(6), 1599-1620 (2001).

3. (with Yang Yin and Liu Weian) On existence of global solutions and blow-up to a system of reaction diffusion equations modeling chemotaxis, SIAM, J. Math. Analysis, 212-241 (2001).

4. (with Luo Zhuangchu) On high dimensional non-linear singular PDE, Acta Math Sinica, 44(1), 2001, 69-76 (in Chinese).

5. (with Yan Zhenbin) Spectral asymptotic behavior for a class of Schrodinger operators on 1-dimensional fractal domains, J. PDE,. 14, 2001, 117-132.

6. (with B. D. Sleeman) High frequency estimates of the Neumann scattering phase in non-smooth obstacle scattering, Inverse Problems, 17, 1-12, 2001.

7. (with L. Rodino) Paradifferential operator in Gevrey classes and its applications, J. Math. Kyoto Univ. 41(1), 1-31, 2001.

8. (with Luo Zhuangchu and H. Tahara) Some new results on nonlinear singular partial differential equations, Operator Theory, Adv. Appl., Vol. 126, 63-71, Birkhaeuser Verlag Basel/Switzerland (2001).

9. (with He Jin-chun) An exact formal solution to reaction-diffusion equations from biomathematics, Wuhan Univ. J. Nat. Sci. 7 (2002), no. 2, 127-132.

10. (with Yang Yin and Liu Weian) Different behaviour for the solutions of 1-dimensional chemotaxis model with exponential growth, Geometry and nonlinear partial differential equations, 181-189, AMS/IP Stud. Adv. Math., 29, Amer. Math. Soc., Providence, RI, (2002).

11. (with Luo Zhuangchu) On the holomorphic solution of non-linear totally characteristic equations with several space variables, Acta Math. Sci. Ser. B Engl. Ed. 22 (2002), no. 3, 393-03.

12. (with Luo Zhuangchu and Zhang Changgui) On the summability of the formal solutions for some PDEs with irregular singularity, C.R.Acad.Sci.Paris, Ser.I, 336 (2003), 219-224.

13. (with Zhong Xinhua) Norm Behavior of Solutions to A Paraboic-Elliptic System Modelling Chemotaxis in a Domain of R^3, Mathematical Methods in the Applied Sciences, 27(2004), 991-1006.

14. (with J. He) The Hamiltonian theory of the Landau-Lifschitz equation with an easy axis, J. Phys. A: Math. Gen., 2004(37), 6311-6318.

15. (with C. Yu) Asymptotic behaviour of the trace for schrodinger operator on irregular domains, Diff. Equ. & Asymptotic Theory (World Scientific), 2004, Series in Anaylsis, Vol. 2, 280-294

16. (with Zhang Zhixiong) On the borel summability of formal solutions for some first order singular PDEs with irregular singularity, Math. Acta Scientia, 2005, 25B(3), 419-426.

17. (with Luo Zhuangchu), Formal solutions for higher order nonlinear totally characteristic pdes with irregular singularities, Contemporary Mathematics Vol. 368:Geometric Analysis of PDE and Several Complex Variables, 121-131, 2005.

18. (with Yang Yin, Liu Weian and B.D. Sleeman) The solvability of some chemotaxis systems, J. Differential Equations 212 (2005) 432-451.

19. (with Zhong Xin-hua), Global existence and blow-up for the solutions to nonlinear parabolic-elliptic system modelling chemotaxis, IMA J. Appl. Math., (2005) 70, 221-240.

20. (with Zhuangchu Luo and Changgui Zhang), On the summability of formal solutions for a class of nonlinear singular PDEs with irregular singularities, Contemporary Mathematics, 400(2006), 53-64 .

21. (with X.H. Zhong), Existence and stability of steady solutions to non -linear parabolic-elliptic systems modeling chemotaxis, Math. Nachr. 279: 13-14(2006), 1441-1447.

22. (with Shaohua Wu), On Existence of Solutions for Some Hyperbolic- Parabolic Type Chemotaxis Systems, IMA J. of Appl. Math., 72 (2007), 1-17.

23. (with Shaohua Wu), The Free Boundary Problem In Biological Phenomena, JPDE, Vol.20, No.2, (2007).

24. （with Shaohua Wu），Hyperbolic-Parabolic Chemotaxis System with Nonlinear Product Terms，JPDE, Vol.21, No.1 (2008).

25. (with Shaohua Wu and Weixi Li), the local and global existence of the solutions of hyperbolic-parabolic system modeling biological phenomena, Acta Math. Scientia, 2008, 28B(1), 101-116.

26. （with Weixi Li），Propagation of Gevrey Regularity for Solutions of Landau Equations，KAM, 1(3), 2008, 355-368.

27. (with Weixi Li and C. J. Xu), Gevrey Hypoellipticity for Linear and Non-linear Fokker-Planck Equations, J. Differential Equations, 246 (2009), 320-339.

28. (with Li Ke) The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations, Math. Nachr. 282, No. 3, 368-358 (2009).

29. （with Zhenya He），Semilinear elliptic equations on Fractal sets, Acta Math. Scientia, 29B(2), 232-242 (2009).

30. (with Weixi Li and C. J. Xu), Gevrey regularity for solution of the spatially homogeneous Landau equation, Acta Math. Scientia, 29B(3), 673-686 (2009).

31. (with Weixi Li and C. J. Xu), Analytic smoothness effect of solutions for spatially homogeneous Landau equation, J. Differential Equations, 248 (2010), 77-94.

32. (with Weixi Li and C. J. Xu), The Gevrey hypoellipticity for a class of kinetic equations, Comm. in PDE, 36(4) (2011), 693-728.

33. (with X. Liu and Y. Wei), Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents, Ann Glob Anal Geom (2011) 39:27–43.

34. (with Weixi Li and C. J. Xu), Gevrey regularity of subelliptic Monge–Ampère equations in the plane，Advances in Mathematics 228 (2011) 1816–1841.

35. (with X. Liu and Y. Wei), Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities, Calculus of Variations and Partial Differential Equations 2012, 43: 463-484.

36. (with X. Liu and Y. Wei), Multiple solutions for semilinear totally characteristic elliptic equations with subcritical or critical cone Sobolev exponents, J. Differential Equations 252 (2012), 4200-4228.

37. (with X. Liu and Y. Wei), Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term, J. Differential Equations 252 (2012), 4289-4314.

38. (with Shaohua Wu), THE MOVING BOUNDARY PROBLEM IN A CHEMOTAXIS MODEL, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 11(2), (2012) 735-746.

39. (with Lingjun Wang), A PERTURBATION APPROACH FOR THE TRANSVERSE SPECTRAL STABILITY OF SMALL PERIODIC TRAVELING WAVES OF THE ZK EQUATION, Kinetic and Related Models, 5(2), (2012) 261-281.

40. (with Yawei Wei and Bin Zhou), Existence of solutions for degenerate elliptic equations with singular potential on conical singular manifolds, Math. Nachr. 285, No.11-12, 1370-1384 (2012).

41. (with Zhuangchu Luo and Changgui Zhang), EXPONENTIAL-TYPE NAGUMO NORMS

AND SUMMABILITY OF FORMAL SOLUTIONS OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS, Ann. Inst. Fourier, Grenoble，62, 2 (2012) 571-618.

42. (with Gongwei Liu), Global existence and nonexistence for semilinear parabolic equations with conical degeneration, J. Pseudo-Differ. Oper. Appl. (2012) 3, 329-349.

43. (with Gongwei Liu), Global existence, uniform decay and exponential growth for a class of semi-linear wave equation with strong damping, Acta Mathematica Scientia 2013, 33B(1), 41-58.

44. (with P. Luo and S.Y. Tian), Existence and Regularity of Solutions to Semi-linear Dirichlet Problem of Infinitely Degenerate Elliptic Operators with Singular Potential Term, Sci China Math, 2013, 56 (4): 687-706, doi: 10.1007/s11425-013-4588-y.

45. (with X. Liu and Y. Wei), Multiple solutions for semi-linear corner degenerate elliptic equations, Journal of Functional Analysis, 266 (2014) 3815–3839.

46. (with Zhuangchu Luo and Changgui Zhang), On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation, Advances in Mathematics 252 (2014), 652-683.

47. (with G. Liu) Global and blow-up E parabolic system with viscoelastic and source terms, Math. Meth. Appl. Sci. 2014, 37, 148–156, DOI: 10.1002/mma.2792.

48. (with P. Luo and S.Y. Tian) Existence and regularity of multiple solutions forinfinitely degenerate nonlinear elliptic equations with singular potential, J. Differential Equations, (2014), published online, DOI: 10.1016/j.jde.2014.06.014.

49. (with P. Luoand G. Liu) Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity, J. of Math. Analysis and Applications, (2014), published online, DOI: 10.1016/j.jmaa.2014.08.030.

50. (with R.H. Qiao, P. Luo, D.Y. Xiao) Lower and upper bounds of Dirichlet eigenvalues for totally characteristic degenerate elliptic operators, SCIENCE CHINA Math. (2014), published online, doi: 10.1007/s11425-000-0000-0.

51. (with P. Luo and S.Y. Tian) Multiplicity and regularity of solutions for in_nitely degenerate elliptic equations with a free perturbation, Journal de Mathématiques Pures et Appliquées, accepted (in press).